Download AP Electrostatics Problems

AP Physics – Electrostatics Problems
1.
1974 (5) The diagram above shows some of
the equipotentials in a plane perpendicular to
two parallel charged metal cylinders. The
potential of each line is labeled.
a. The left cylinder is charged positively.
What is the sign of the charge on the
other cylinder?
b. On the diagram above, sketch lines to
describe the electric field produced by
the charged cylinders.
c. Determine the potential difference,
VA - VB, between points A and B.
d. How much work is done by the field if a charge of 0.50 C is
moved along a path from point A to point E and then to
point D?
2.
1975 (2) Two identical electric charges +Q are located at two
corners A and B of an isosceles triangle as shown to the right.
a. How much work does the electric field do on a small test charge +q as the charge moves from point
C to infinity,
b. In terms of the given quantities, determine where a third charge +2Q should be placed so that the
electric field at point C is zero. Indicate the location of this charge on the diagram above.
3.
1978 (3) A uniform electric field E is established between two
capacitor plates, each of area A, which are separated by a distance
s as shown to the right.
a. What is the electric potential difference V between the plates?
b. Specify the sign of the charge on each plate.
The capacitor above is then connected electrically through a resistor to a second parallel-plate capacitor,
initially uncharged, whose plates have the same area A but a separation of only s/2.
c. Indicate on the diagram below the direction of the current in each wire, and explain why the current
will eventually cease.
d. After the current has ceased, which capacitor has the greater charge? Explain your reasoning.
e. The total energy stored in the two capacitors after the current has ceased is less than the initial stored
energy. Explain qualitatively what has become of this “lost” energy.
4.
1979 (4) Determine the magnitude and direction of the force on a
proton in each of the following situations. Describe qualitatively the
path followed by the proton in each situation and sketch the path on
each diagram. Neglect gravity.
a. The proton is released from rest at the point P in an electric
field E having intensity 104 N/C and directed up in the plane of
the page as shown to the right.
b. In the same electric field as in part (a), the proton at point P has
velocity v = 105 m/s directed to the right as shown to the right.
5.
1980 (5) An unstable nucleus, initially at rest, decays into two
spherical fragments. Fragment A has radius rA charge qA, and rest
mass mA; fragment B has radius rB, charge qB, and rest mass mB.
a. Suppose that after the decay process fragment A has velocity vA
that is small-compared with the velocity of light. Develop an
expression for the kinetic energy of fragment B in terms of vA,
mA, and mB.
At one stage in the decay process, the two fragments may be regarded
as touching spheres, both at rest as shown above. Write expressions
for each of the following.
b. The electrostatic force between these two fragments at the instant
they are touching.
c. The electrostatic potential energy, U, of this two fragment system at the instant they are touching.
6.
1981 (3) A small conducting sphere of mass 5 x 10-3 kg,
attached to a string of length 0.2 m, is at rest in a
uniform electric field E, directed horizontally to the
right as shown above. There is a charge of 5 x 10-6 C on
the sphere. The string makes an angle of 30° with the
vertical. Assume g = 10 N/C.
a. Draw and label all the forces acting on the sphere.
b. Calculate the tension in the string and the
magnitude of the electric field.
c. The string now breaks. Describe the subsequent motion
of the sphere and sketch on the following diagram the
path of the sphere while in the electric field.
7.
1982 (7) Consider the Millikan Oil Drop Experiment.
Write an account of this experiment. Include in your account:
a. a labeled diagram of the experimental setup.
b. a discussion of the experimental observations.
c. the important conclusions of the experiment.
8.
1985 (3) An electron initially
moves in a horizontal direction and
has a kinetic energy of 2.0 x 103 eV
when it is in the position shown
above. It passes through a uniform
electric field between two
oppositely charged horizontal
plates (region I) and a field-free
region (region II) before eventually
striking a screen at a distance of
0.08 m from the edge of the plates.
The plates are 0.04 m long and are
separated from each other by a
distance of 0.02 m. The potential difference across the plates is 250 volts. Gravity is negligible.
a. Calculate the initial speed of the electron as it enters region I.
b. Calculate the magnitude of the electric field E between the plates, and indicate its direction,
c. Calculate the magnitude of the electric force F acting on the electron while it is in region I.
d. Sketch the path of the electron in regions I and II. For each region describe the shape of the path.
9.
1987 (2) Object I, shown above, has a
charge of + 3 × 10-6 C and a mass of
0.0025 kg.
a. What is the electric potential at point
P, 0.30 m from object I?
Object II, of the same mass as object
I, but having a charge of +1 × 10-6 C
is brought from infinity to point P, as
shown above.
b. How much work must be done to
bring the object II from infinity to
point P ?
c. What is the magnitude of the electric force between the two objects when they are 0.30 meter apart?
d. What are the magnitude and direction of the electric field at the point midway between the two
objects?
The two objects are then released simultaneously and move apart due to the electric force between them.
No other forces act on the objects.
e. What is the speed of object I when the objects are very far apart?
10.
1989 (2) Two point
charges, Q1 and Q2, are
located a distance 0.20
m apart, as shown above. Charge Q1 = +8.0 µC. The net electric field is zero at point P, located 0.40 m
from Q1 and 0.20 m from Q2.
a. Determine the magnitude and sign of charge Q2.
b. Determine the magnitude and direction of the net force on charge Q1
c. Calculate the electrostatic potential energy of the system.
d. Determine the coordinate of the point R on the x-axis between the two charges at which the electric
potential is zero.
e. How much work is needed to bring an electron from infinity to point R. which was determined in the
previous part?
11.
1990 (2) A pair of square
parallel conducting plates,
having sides of length 0.05
m, are 0.01 m apart and are
connected to a 200 V
power supply, as shown to
the right. An electron is
moving horizontally with a
speed of 3 × 107 m/s when it enters the region between the plates. Neglect gravitation and the distortion
of the electric field around the edges of the plates.
a. Determine the magnitude of the electric field in the region between the plates and indicate its
direction on the figure above.
b. Determine the magnitude and direction of the acceleration of the electron in the region between the
plates.
c. Determine the magnitude of the vertical displacement of the electron for the time interval during
which it moves through the region between the plates.
d. Sketch the path of the electron as it moves through and after it emerges from the region between the
plates.
12.
1993 (2) A charge Q1 = -16 × 10-6 C is fixed on the x-axis at
+4.0 m, and a charge Q2 = + 9 × 10-6 C is fixed on the y-axis at
+3.0 m, as shown on the diagram to the right.
a.
i. Calculate the magnitude of the electric field E1 at the
origin O due to charge Q1
ii. Calculate the magnitude of the electric field E2 at the
origin O due to charge Q2.
iii. On axes like those below, draw and label vectors to show
the electric fields E1 and E2 due to each charge, and also
indicate the resultant electric field E at the origin.
a. Calculate the electric potential V at the origin.
A charge Q3 = -4 × 10-6 coulomb is brought from a very
distant point by an external force and placed at the origin.
b. On axes like those to the right, indicate the direction of
the force on Q3 at the origin.
c. Calculate the work that had to be done by the external
force to bring Q3 to the origin from the distant point.
13.
1996 (6) Robert Millikan received a Nobel Prize for
determining the charge on the electron. To do this, he set
up a potential difference between two horizontal parallel
metal plates. He then sprayed drops of oil between the
plates and adjusted the potential difference until drops of a
certain size remained suspended at rest between the plates,
as shown above. Suppose that when the potential
difference between the plates is adjusted until the electric field is 10,000 N/C downward, a certain drop
with a mass of 3.27 × 10-16 kg remains suspended.
a. What is the magnitude of the charge on this drop?
b. The electric field is downward, but the electric force on the drop is upward. Explain why.
c. If the distance between the plates is 0.01 m, what is the potential difference between the plates?
d. The oil in the drop slowly evaporates while the drop is being observed, but the charge on the drop remains the
same. Indicate whether the drop remains at rest, moves upward, or moves downward. Explain briefly.
14.
1998 (2) A wall has a negative charge
distribution producing a uniform
horizontal electric field. A small plastic
ball of mass 0.01 kg, carrying a charge
of -80.0 µC, is suspended by an
uncharged, nonconducting thread 0.30 m
long. The thread is attached to the wall
and the ball hangs in equilibrium, as
shown above, in the electric and gravitational fields. The electric force on the
ball has a magnitude of 0.032 N.
a. Draw and label the forces acting on
the ball.
b. Calculate the magnitude of the electric field at the ball's location due to the charged wall, and state
its direction relative to the coordinate axes shown.
c. Determine the perpendicular distance from the wall to the center of the ball.
d. The string is now cut.
i. Calculate the magnitude of the resulting acceleration of the ball, and state its direction relative to
the coordinate axes shown.
ii.
Describe the resulting path of the ball.
15.
1999 (2) In a television set, electrons are first accelerated from rest through a potential difference in an
electron gun. They then pass through deflecting plates before striking the screen.
a. Determine the potential difference through which the electrons must be accelerated in the electron
gun in order to have a speed of 6.0 × 107 m/s when they enter the deflecting plates.
The pair of horizontal plates shown
below is used to deflect electrons up
or down in the television set by
placing a potential difference across
them. The plates have length 0.04 m
and separation 0.012 m, and the right
edge of the plates is 0.50 m from the
screen. A potential difference of 200
V is applied across the plates, and the
electrons are deflected toward the top
of the screen. Assume that the electrons enter horizontally midway between the plates with a speed of
6.0 × 107 m/s and that fringing effects at the edges of the plates and gravity are negligible.
b. Which plate in the pair must be at the higher potential for the electrons to be deflected upward.
Justify your answer.
c. Considering only an electron's motion as it moves through the space between the plates, compute the
following.
i. The time required for the electron to move through the plates
ii. The vertical displacement of the electron while it is between the plates
d. Show why it is a reasonable assumption to neglect gravity in part c.
e. Still neglecting gravity, describe the path of the electrons from the time they leave the plates until
they strike the screen. State a reason for your answer.
Quantitative answers to selected questions
1.
2.
3.
4.
(1974, #5)
(1975, #2)
(1978, #3)
5.
(1980, #5 a, b, c)
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
(1981, #3)
a. positive c. -10 V d. -15 J
a. 1.8 × 1010 N·m2/C2(qQ/a) b. 2a above C
a. E·s d. the capacitor on the right
kqA qB
kqA qB
m A 2 vA 2
b.
c.
2
(rA + rB )
rA + rB
2mB
3
b. 0.058 N c. 5.8 × 10 N/C
a.
(1985, #3) a. 2.65 × 107 m/s b. 1.25 × 104 V/m c. 2.0 × 10-15 N
(1987, #2) a. 9.0 × 104 V b. 0.09 J c. 0.3 N d. 8.0 × 105 N/C, to the right e. 6 m/s
(1989, #2) a. -2 µC b. 3.6 N to the right c. -0.72 J d. 0.16 m e. 0
(1990, #2, parts a-d) a. 2 × 104 V/m b. 3.5 × 1015 m/s2 upward c. 4.9 × 10-3 m
(1993, #2) a. i. 9.0 × 103 N/C, ii. 9.0 × 103 N/C b. -9.0 × 103 V
d. 3.6 × 10-2 N/C
(1996, #6) a. 3.27 × 10-19 C
b. negative
c. 100 V
d. upward
(1998, #2) b. 400 N/C to the left c. 0.09 m d. i. 72° below the x-axis
(1999, #2) a. 1.0 × 104 V
b. upper
c. i. 6.7 × 10-10 s, ii. 6.5 × 103 m